The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiat...

Learning vector calculus techniques is one of the major hurdles faced by physics undergraduates. However, beginners report various difficulties dealing with index notation due to its bulkiness. Meanwhile, there have been graphical notations for tensor algebra that are intuitive and effective in calculations can serve as a quick mnemonic algebraic identities. Although they introduced applied edu...

The quasidifferential calculus developed by V.F. Demyanov and A.M. Rubinov provides a complete analogon to the classical calculus of differentiation for a wide class of nonsmooth functions. Although this looks at the first glance as a generalized subgradient calculus for pairs of subdifferentials it turns out that, after a more detailed analysis, the quasidifferential calculus is a kind of Fréc...

FRACTIONAL calculus has been applied in all MAD (modeling, analysis and design) aspects of control systems engineering since Shunji Manabe’s pioneering work in early 1960s. The 2016 International Conference on Fractional Differentiation and Its Applications (ICFDA) was held in Novi Sad, Serbia, July 18-20. Quoting from the website http://www.icfda16.com/ “Fractional Calculus (FC for short) is a...

The main goal of this article is to study the extend Struve and extended modified matrix functions by making use Beta function. In particular, we investigate certain important properties these such as integral representation, differentiation formula hypergeometric representation functions. Finally, obtain some results on transform fractional calculus

Differential categories are now an established abstract setting for differentiation. The paper presents the parallel development for integration by axiomatizing an integral transformation, sA : !A→ !A⊗A, in a symmetric monoidal category with a coalgebra modality. When integration is combined with differentiation, the two fundamental theorems of calculus are expected to hold (in a suitable sense...

This chapter presents a visual process calculus for designing and simulating computer models of biological systems. The calculus is based on a graphical variant of stochastic pi-calculus, extended with mobile compartments, and the simulation algorithm is based on standard kinetic theory of physical chemistry. The calculus forms the basis of a formal visual programming language for biology. The ...

Abstract A scheme for the analytical stochastization of ordinary differential equations (ODEs) is presented in this article. Using Itô calculus, an ODE transformed into a stochastic equation (SDE) such way that solutions obtained can be constructed. Furthermore, constructed trajectories remain bounded same interval as deterministic solutions. The proposed approach stark contrast to methods base...